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Suspended-core fibers are systematically studied. We show that confinement loss in suspended-core fibers can be effectively reduced by an increase of air-cladding width for even sub-micron core diameters and, therefore, provides a considerable simpler solution than equivalent photonic crystal fibers with a large number of air holes for a wide range of nonlinear applications. We have further demonstrated a suspended-core silica fiber with core diameters of 1.27µm and sub-dB splice loss to Hi1060. Loss at 1.55µm was measured in this fiber to be 0.078dB/m, a record for this small core diameter, limited mainly by scattering loss at the glass and air interface. The combination of high nonlinearity, low splice loss and low transmission loss of the suspended core silica fibers will enable a new class of low loss all-fiber nonlinear devices.
©2008 Optical Society of America
1. Introduction
Photonics crystal fibers (PCFs) with a matrix of periodic air holes in the cladding have significantly increased the achievable NAs of an optical fiber. In a PCF with very large air filling factor, NA of close to 1 can be achieved, compared to the ~0.35 achievable in a conventional fiber, limited by the level of dopants which can be incorporated. This much increased NA enables not only highly nonlinear optical fibers with much smaller mode field diameters (MFD) [1, 2], but also, more importantly, anomalous dispersion at much shorter wavelength. The availability of optical fibers with anomalous dispersion close to the very important wavelength of ~800nm, where high energy femto-second pulses are readily available from a Ti-Sapphire system, re-ignited the interests in super-continuum generation to a new level unseen since its initial observations some thirty years earlier [3,4].
The matrix of periodic air holes implied in a PCF is, however, not essential in the implementation of fibers with very high NAs, required by a variety of works using optical nonlinear effects including super-continuum generation. Suspended core fibers (SCF), first reported by Kiang et al in 2002 [5] with lead silicate glass, followed by Ravi Kanth Kumar et al and Petropoulos et al in 2003 with tellurite and lead silica glasses respectively [6, 7], demonstrate an interesting alternative for implementing fibers with high NAs. A SCF has a cladding consisting essentially of air and not only is much simpler, therefore potentially easier to make, but also offers potential for higher NAs, therefore enabling designs with even smaller MFDs and shorter zero dispersion wavelength. These extremely high NAs can be difficult to make with PCFs due to the practical limit of air filling factor achievable using a hexagonal stack of capillaries. In these first demonstrations, core diameter down to 2.0µm was reported by Kiang et al [5], 2.6µm by Ravi et al [6] and 1.7µm by Petropoulos et al [7], losses of several dB/m was expected or measured. Extrusion technique was exclusively used. Recently, extremely broad band super-continuum generation has been demonstrated in soft glass SCFs [8, 9]. Although soft glasses offer substantially higher nonlinear coefficient, silica fibers usually provide better overall figure of merit due to the two or four orders of magnitudes longer fiber that can be used for the same insertion loss. Silica SCFs was not demonstrated until 2006 by Mukasa et al [10]. Three holes were drilled in a high purity silica VAD rod. The holes were mechanically polished. SCFs with triangular cores with diameters as small as 0.8µm and 0.9µm were drawn. The SCF with 0.9µm core has shown a loss as low as 180dB/km at 1.55µm. This is the lowest ever loss reported at this small core diameter, demonstrating the potential of SCFs.
In this paper, we have systematically studied the potential of SCFs for ultra small MFD fibers with low splice and transmission losses and their dispersion properties. We found that low confinement loss is not an issue if the width of the air cladding is increased, even for sub-wavelength core diameters. We have demonstrated silica SCFs with core diameter of 1.27µm, with loss of 78dB/km at 1550nm, limited mainly by glass and air interface scattering loss. This is the lowest loss ever reported at this small core diameter. These SCFs were fabricated by a modified stack-and-draw technique with expansion of air holes in both caning and fiber drawing phases for the first time, providing much improved surface quality and ease of fabrication. We have also demonstrated that the small core SCFs can be spliced to Hi1060 with sub-dB splice loss for core diameter as small as 1.27µm.
2. Motivations
The first motivation of this work is to maximize nonlinear coefficient by minimizing near-field rms mode field diameter (MFD). MFD at a wavelength of 1µm for step-index fibers with various NAs are studied with a full vector mode solver based on the transfer matrix technique (see Fig. 1(a)) [11]. Please note that NA is defined as NA=(n2 co-n2 cl)1/2, where nco and ncl are the refractive indexes of core and cladding respectively, and can exceed 1 numerically. It should be noted that, for silica core suspendered in air with nco=1.45 and ncl=1, NA is1.05. It can be seen that smaller MFD can be achieved at high NAs with MFD=0.79µm at a wavelength of 1µm possible with a NA=1.05. MFD decreases with wavelength as shown in Fig. 1(b) with MFD=0.39µm possible at a wavelength of 0.5µm in a step-index fiber with NA=1.05.
Fig. 1. (a). MFD at 1µm versus V value for step-index fibers with various NAs, (b) MFD versus V value at various wavelengths for a step-index fiber with a NA of 1.05.
Fig. 2. (a). Waveguide dispersion in step-index fibers with various NAs, (b) Material dispersion of fused silica, along with the minimum 1st zero dispersion wavelengths λ01 marked out by symbols for step-index fibers with various NAs. The V value of each fiber required to achieve the minimum λ01 is listed in the legends.
PCFs have been widely credited as the enabling technology for ultra broad super-continuum generation (SCG). It is worth noting that the most significant enabling property for SCG is PCFs’ ability to shift the 1st zero dispersion wavelength λ01 towards shorter wavelength so that anomalous dispersion can be realized close to wavelengths where high energy femto-second pulses are available from a Ti-Sapphire system. It has been also realized that shorter λ01 is desirable for efficient SCG at the very interesting visible and UV wavelengths. The 2nd motivation of this work is to realize fibers with minimum λ01. Waveguide dispersion versus V value is plotted for step-index fibers with various NAs in Fig. 2(a). To cancel normal material dispersion in the short wavelength regime, anomalous waveguide dispersion (positive in ps/nm/km unit) is required. The larger the anomalous waveguide dispersion is, the shorter λ01 can be realized. It should be noted that the maximum of the anomalous waveguide dispersion can be shifted to appropriate wavelength by dimensional scaling. It can be seen from Fig. 2(a) that anomalous dispersion can only be realized in the multimode regime of V>2.405. The anomalous dispersion reaches a peak at V=4.8 for NA=1.05 and this peak moves to progressive larger V value in fibers with lower NAs. Fibers with higher NAs also have larger anomalous waveguide dispersion and are capable of moving λ01 to shorter wavelength. Material dispersion for fused silica is plotted in Fig. 2(b). To get minimum λ01, we need to operate at V>2.405, where mode is well confined to silica glass. Minimum λ01 for fibers with various NA can then be obtained. Symbols mark the minimum λ01 that can be achieved at each NAs. For silica fibers, the minimum achievable λ01 is 553nm in a fiber with NA=1.05. The V value of each fiber to realize the minimum λ01 is given in the legends. This is also the V value at the anomalous waveguide dispersion peak in Fig. 2(a).
3. Confinement loss and dispersion
As we are interested in SCFs with very small MFDs, confinement loss needs to be managed to realize low loss fibers especially for fibers with core diameters of less than 2µm. It has been well know that confinement loss decreases very fast with each additional layer of air holes in a PCF [12]. In SCFs, glass webs can be made to be a very small fraction of optical wavelength, so they would no longer play an active role at the optical frequency. We simulated SCFs with a silica core with diameter 2ρ=1µm and refractive index nco=1.45. The silica core is surrounded by an air cladding with ncl=1 and width d as shown in the inset of Fig. 3 and the air cladding is further surrounded by an silica outer layer with n0=1.45. We have again used the full vector mode solver based on the transfer matrix technique. We have added further slightly lossy outer layer with a refractive index nco=1.45+10-8i, enclosing the entire fiber with its outer silica layer so that the confinement loss can be simulated (please note that the small imaginary part is just for numerical stability as a well known numerical technique and has no consequence on confinement loss if placed suitable distance away from the guided modes, see [13] for further details). The SCFs with various air-cladding width d are studied for its confinement loss. Both dispersion and confinement loss versus normalized wavelength λ/2ρ and corresponding V value are plotted in Fig. 3. Dispersions in fibers with various air-cladding widths do not change much with varying d and essentially overlap each other. The confinement losses, on the other hand, can be significantly lowered by an increase in air-cladding width d as shown in Fig. 3 when d is changed from 5µm to 15µm in 2.5µm steps. Corresponding V value of the fibers are shown in the upper horizontal axis. Confinement losses increase with an increase of wavelength or a decrease of V value, as a consequence of a reduction of confinement of the finite air cladding.
Fig. 3. Confinement loss of SCFs with air-cladding width d=5, 7.5, 10, 12.5, and 15µm, lines with symbols, are shown on right vertical axis. Corresponding waveguide dispersions, lines, are shown on left vertical axis. The dispersion curves remain mostly the same with a change of d.
Fig. 4. (a). Confinement loss versus normalized air-cladding width d/2ρ at various normalized wavelengths, λ/2ρ. Simulation is performed for 2ρ=1µm at various wavelengths. (b). Normalized field for d=15µm and 2ρ=1µm at various normalized wavelengths.
The rapid decay of confinement losses versus normalized air-cladding width d/2ρ are clearly seen for three normalized wavelengths in Fig. 4(a). Normalized field distributions at various normalized wavelengths are plotted in Fig. 4(b) for the fiber with d=15µm, showing rapid decay of the modal fields in the air cladding. Increase of air-cladding width can therefore be effectively used to reduce confinement loss to a negligible level even for sub-micron core diameters.
Total dispersion of SCFs at various core diameters are further studied with 6 hexagonally positioned circular air holes with diameter to pitch ratio of 0.99. This geometry is very close to SCFs made with six air holes. The simulation was done with a Multipole mode solver similar to that in [13]. Core diameter is defined as the nearest distance between two opposing holes (see inset of Fig. 5). Material dispersion was considered with the empirical formula describe in [14]. The total dispersion of the SCFs is plotted in Fig. 5 versus wavelength for core diameters from 0.6µm to 2µm in 0.2µm steps. The 1st zero dispersion wavelength moves progressively towards shorter wavelength with λ01=~565nm for 2ρ=0.6µm, very close to the theoretical limit of 553nm. It is also worth noting that the 2nd zero dispersion wavelength λ02 moves towards shorter wavelength at an even faster rate. Both λ01 and λ02 would disappear at smaller core diameters, leaving no overall anomalous dispersion regime.
Fig. 5. (a). Waveguide dispersion for SCFs with various core diameters. Inset shows the fiber structure studied, six air holes in a hexagonal grid with d/Λ=0.99. Core diameter 2ρ is given in the legends.
4. Experiment
We have fabricated a large number of silica SCFs by stacking 6 silica capillaries around a central silica. In some cases, the central silica rod has a highly germanium-doped center, which is used to achieve an enhanced nonlinearity in the SCFs. The 6 air holes are expanded during a caning stage and further expanded in the fiber drawing. This two-stage process is unique in that it allows significant expansion of the air holes from the initial preform.
Three SCFs are studied for transmission loss. SCF1 has a core diameter of 2ρ=2.3µm with a pure silica core. SCF2 has a similar core diameter of 2ρ=2.3µm. Its center part of the core, ~60% of core diameter, is doped with graded index germanium-doped area with NA=0.275 (supplied by J-Fiber). SCF3 has a core diameter of 2ρ=1.27µm. Its center part of the core is similarly doped with germanium as in SCF2. The transmission loss of all three SCFs is shown in Fig. 6. The transmission loss of the SCF1 has less defect related losses due to the pure silica core. It is well fitted with the λ-3 dependence, associated with core and cladding interface scattering loss [15]. Bulk Rayleigh scattering with its λ-4 dependence is expected to contribute very little to the measured loss due to the high purity silica glass used here. It is, therefore, reasonable to conclude that its transmission is dominated by scattering loss at the air and glass boundary. SCF2 has a clear stronger short wavelength loss below ~1µm as well as a slightly higher loss at longer wavelength above 1.55µm. The additional short wavelength loss increase faster than λ-4 and may be from germanium-related defects. SCF3 has in general a much higher loss. SCF3 also shows a minimum loss at ~1.55µm. The minimum loss of 78dB/km in SCF3 is the lowest loss ever reported in a fiber with this small core diameter of 1.27µm. No significant confinement loss was observed in any of these fibers except possibly SCF3. It would increase strongly with an increase of wavelength. All these SCFs are multimode in the wavelength range studied.
Fig. 6. Measured loss for three fibers; SCF1: 2ρ=2.3µm, no germanium in the core; SCF2: 2ρ=2.3µm, germanium doped center of ~60% core radius, graded refractive index with NA=0.275, SCF3: 2ρ=1.27µm, with germanium-doped center similar to SCF2. Close up of SCF1 is essentially the same as SCF2. A global view is used to show the whole fiber instead. The solid line fit is of the formula: A+B/λ3.
A fourth fiber, SCF4, was used for dispersion and birefringence study. SCF4 has slightly distorted core with 2ρ=2.3µm along the two large holes and 2ρ=2.8µm along two smaller holes (see fiber cross section in the inset of Fig. 7). The results in crosses are shown in Fig. 7 along with simulated dispersion for the two polarization modes. The core is elliptical in this case, causing the two polarization modes to become non-degenerate. The simulation was done with the Multipole mode solver using six air holes simulating the outer boundary of the core (see bottom inset of Fig. 7). The simulation fits well with measured data, demonstrating the dispersion is mostly governed by the outer shape of the core at core and cladding boundary. This is obviously no longer valid in regime of very weak core guidance, where modal field spreads away from the core and consequently, probing more of the structures further away form the core and cladding boundary. Simulated mode field at 1.05µm is also shown in the inset of Fig. 7.
Birefringence in SCF4 was also measured. Ytterbium ASE source polarized at 45° to the polarization axis of the fiber was launched into 66cm of SCF4. The output passes through a second polarizer set at 45° to the fiber polarization axis before enters an OSA. Fringe pattern with over 25dB contrast with 1.26nm spacing was measured (see top inset in Fig. 7), giving a group birefringence Δn=9.8×10-4 at 1020nm, comparing reasonably with the predicted group birefringence 7.9×10-4.
Small core of the SCFs enables high nonlinearity. SCF3 with a core diameter of 1.27µm has an effective mode area of 1.1µm2 and 1.75µm2 at 1.05µm and 1.55µm respectively. This gives an estimated γ=~140 1/W/Km and ~60 1/W/Km at 1.05µm and 1.55µm respectively, assuming n2=2.6×10-20 m2/W. In our fiber, since mode is well confined in the silica glass, the effect of air is ignored. SCF1, SCF2 and SCF4 would have γ=~50 1/W/Km at ~1µm. The SCFs was further demonstrated to be capable of splicing to Hi1060 via an intermediate fiber (Nufern, NA=0.35, diameter=2.1µm) with reasonable low loss. Total loss for two splices (Hi1060 to High NA, High NA to SCF4) for SCF4 was measured to be as low as ~0.25dB. Total loss for SCF3 with 2ρ=1.27µm was measured to be as low as ~0.8dB.
Fig. 7. Measured dispersion and simulated Multipole result with using six air holes as shown in the bottom inset. Index difference between the two polarization modes is also shown. A simulated mode at 1.05µm is also shown in the bottom inset. The top inset shows measured fringe pattern from interference of the two birefringence modes.
Super-continuum generation was also demonstrated in SCF4. An ytterbium-doped fiber laser which provides 350fs pulses at 200KHz repetition rate at 1045nm was used. Octave-spanning super-continuum from 600nm to 1300nm was observed in 1.3m SCF4 at a very low peak power of ~2kW. This is a record low pump power for octave-spanning super-continuum at the pump wavelength of ~1µm and it, consequently, eliminates the need for amplification in a fCEO-stabilized ytterbium fiber oscillator using a self-reference scheme [16]. Details of super-continuum generation will be reported in [17].
5. Conclusion
We have systematically studied SCFs for the potential for highly nonlinear fibers due to the extremely high NA possible with SCFs. In a silica SCF, NA as high as 1.05 can be realized, giving a minimum MFD of 0.79µm at 1µm, i.e. effective mode area of 0.49µm2, potentially enabling γ≈330 1/km/W for silica SCFs with n2=2.6×10-20 m2/W. We have shown that the minimum 1st zero dispersion wavelength is λ01=553nm for silica fibers, limited by maximum achievable anomalous waveguide dispersion. We have further shown that an increase the air-cladding widths is an effective way of reducing confinement loss, rendering confinement not an issue with practical air-cladding width. Several silica SCFs were fabricated. In a SCF with 1.27µm core diameter, loss as low as 78 dB/km was measured at 1.55µm and was found to be mainly limited by interface scattering loss. A low splice loss of 0.8 dB to Hi1060 fiber via a high NA fiber was realized in this fiber, opening doors for compact all-fiber nonlinear devices with exceptionally low insertion losses. Octave-spanning super-continuum has also been demonstrated at very low peak power of ~2kW for a pump wavelength of 1045nm.
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